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%% Linearity of Scaling Exponents for Monofractal Signal % Confirm that for a monofractal signal, the scaling exponents % are a linear function of the moments. For multifractal signals, the % exponents are a nonlinear function of the moments. %% % Load a signal that contains two time series, each with 8000 samples. % |Ts1| is a multifractal signal and |Ts2| is a monofractal fractional % Brownian signal. Obtain the exponents using |wtmm|. load RWdata; [hexp1,tauq1] = wtmm(Ts1); [hexp2,tauq2] = wtmm(Ts2); %% % Plot the scaling exponents. expplot = plot(-2:0.1:2,tauq2,'b-o',-2:0.1:2,tauq1,'r-^'); grid on; expplot(1).MarkerFaceColor = 'b'; expplot(2).MarkerFaceColor = 'r'; legend('Ts2-Monofractal','Ts1-Multifractal','Location','SouthEast'); title('Monofractal vs. Multifractal Scaling Exponents'); xlabel('Qth Moment'); ylabel('Scaling Exponents'); %% % |Ts2|, which is the monofractal signal, is a linear function. |Ts1|, the % multifractal signal, is not linear.